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1.5 Trigonometry

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Question 46

A mechanical component for a precision pendulum clock is designed using a triangular metal plate OAB OAB\,OAB attached to a weighted circular sector OBC OBC\,OBC with centre OOO.

In this design:

  • OB=6.5 cmOB = 6.5\text{ cm}OB=6.5 cm
  • AB=3.5 cmAB = 3.5\text{ cm}AB=3.5 cm
  • angle AOB=π12\displaystyle AOB = \frac{\pi}{12}AOB=12π​ radians
  • angle OAB OAB\,OAB is an obtuse angle
a.

Determine the size of angle OABOABOAB, giving your answer in radians to 4 significant figures.

[3]
b.

Calculate the area of the triangular plate OAB OAB\,OAB in cm2\text{cm}^2cm2, giving your answer to 3 significant figures.

[2]
c.

Given that the ratio of the area of the weighted sector OBC OBC\,OBC to the area of the triangular plate OAB OAB\,OAB is 7:4 7:4\,7:4

Show that angle BOC BOC\,BOC is 0.224 radians to 3 significant figures.

[3]
d.

Hence find the total perimeter of the component, in cm, to the nearest integer.

[3]
Markscheme

1.5 Trigonometry Questions

  1. A Level
  2. /Maths
  3. /1.5 Trigonometry

317 exam-style questions on OCR A Level Maths 1.5 Trigonometry, covering 1.5.1 Definitions for all arguments, 1.5.2 Sine and cosine rules, 1.5.3 Area of a triangle, 1.5.4 Radian measure (A-level only), 1.5.5 Small angle approximations (A-level only), 1.5.6 Graphs of basic trigonometric functions, 1.5.7 Exact values in radians (A-level only), 1.5.8 Reciprocal and inverse trigonometric ratios (A-level only), 1.5.9 Graphs of reciprocal and inverse functions (A-level only), 1.5.10 Trigonometric identities, 1.5.11 Further trigonometric identities (A-level only), 1.5.12 Double angle and compound angle formulae (A-level only), 1.5.13 Geometrical proofs of formulae (A-level only), 1.5.14 Harmonic form Rcos / Rsin (A-level only), 1.5.15 Trigonometric equations, 1.5.16 Proof involving trigonometric functions (A-level only), and 1.5.17 Trigonometric functions in context. Each one has a worked solution and a mark scheme showing where the marks go.

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